perspicuous, the solutions neat and short. They also presume, that the numerous and diversified exercises which this book contains, are all such as may, and do daily occur in practice; that they are well adapted to their respective rules; so clearly expressed, that they cannot be misunderstood; and so carefully arranged, as to lead the learner on, step by step, from what is easy, to what is more difficult : while they contain nothing that can tend to perplex and discourage him in his progress. Many short and easy methods of computation are here explained and exemplified; the reasons of the rules are also briefly but clearly stated; and illustrations of commercial subjects are given wherever such information appeared necessary, or was likely to be useful. In short, the Editors have endeavoured to compress as much pertinent information as possible into this volume; and they confidently hope that it will be found to contain every thing requisite, in a text book, in order to facilitate the attainment of an art, than which none is of greater value, or of more extensive utility. The Editors intend to put to Press without delay, a Key to this System of Arithmetic, containing Solutions of all the Exercises. CHARACTERS USED IN THE FOLLOWING TRACT. = (equal to) denotes equality; thus, 20/=£1. + (plus) (minus) denotes addition; thus, 2+5=7. × (multiplied by) denotes multiplication; 'thus, 2×3=6. (divided by) denotes division; thus, 12—4—3. ✔(radical sign) denotes the square root; thus, 3 4-2. ✔ denotes the cube root; " denotes the nth root; and so on. When a number is multiplied any number of times into itself, the number of factors is generally denoted by a small figure written at the upper corner on the right hand of the number: thus, 22 denotes 2x2; 63 denotes 6×6×6; and so on. The sign x is sometimes omitted: thus, abc denotes axbxc; and 4 a denotes 4xa. Instead of the sign, division is frequently denoted by writing the quantities in the form of a fraction: thus, either 13 4 or 13 denotes the quotient of 13 divided by 4. When several numbers are included within a parenthesis, they are to be taken collectively: thus, (7+5)×6 denotes that the sum of 7 and 5 is to be multiplied by 6. The root of a number is sometimes denoted by a fraction written at the upper corner on the right hand of the number: thus, 71=√7; 7*=3√/7; 733/72; and so on. 3 = |